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Proof WritingHardPigeonhole and Extremal Arguments

Pigeonhole and Extremal Arguments · Hard problem

A student writes: "Among any 55 numbers from {1,2,…,9}\{1, 2, \ldots, 9\} two are consecutive. Boxes: {1,2},{3,4},{5,6},{7,8},{9}\{1, 2\}, \{3, 4\}, \{5, 6\}, \{7, 8\}, \{9\}." Which verdict is right?

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